| gpt4 | |
| --- | |
| I'm doing Prolog experiments. | |
| The grid is 1-indexed. | |
| Top-Left Bottom-Right (TLBR) is used for object bounding boxes, like tY_lX_bY_rX where t=top l=left b=bottom r=right. | |
| The width of the object bounding box has a 'w' prefix, like 'w5' is width=5. | |
| The height of the object bounding box has a 'h' prefix, like 'h3' is height=3. | |
| The `id` prefixed text has no integer value and should not be considered. | |
| Consider both euclidian distance and manhatten distance between objects, since it may impact the `id` assigned to the object. | |
| ```prolog | |
| % Example 1 input grid_width20_height30 | |
| object(input1_idPz7ea0g_t18_l15_b18_r15_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idPz7ea0g_t13_l15_b13_r15_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idP48kmo7_t28_l5_b28_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idP48kmo7_t19_l5_b19_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idPj8kdf4_t21_l8_b21_r8_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idPj8kdf4_t21_l3_b21_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idP33ffe7_t7_l12_b7_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idP33ffe7_t7_l4_b7_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idPfe7a8k_t14_l7_b14_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input1_idPfe7a8k_t3_l7_b3_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| % Example 1 output grid_width20_height30 | |
| object(output1_idPz7ea0g_t13_l15_b18_r15_w1_h6_mass6_shapeRectangle_scalex1_scaley6, transform(all)). | |
| object(output1_idP48kmo7_t19_l5_b28_r5_w1_h10_mass10_shapeRectangle_scalex1_scaley10, transform(all)). | |
| object(output1_idPj8kdf4_t21_l6_b21_r8_w3_h1_mass3_shapeRectangle_scalex3_scaley1, transform(all)). | |
| object(output1_idPj8kdf4_t21_l3_b21_r4_w2_h1_mass2_shapeRectangle_scalex2_scaley1, transform(all)). | |
| object(output1_idP33ffe7_t7_l8_b7_r12_w5_h1_mass5_shapeRectangle_scalex5_scaley1, transform(all)). | |
| object(output1_idP33ffe7_t7_l4_b7_r6_w3_h1_mass3_shapeRectangle_scalex3_scaley1, transform(all)). | |
| object(output1_idPfe7a8k_t3_l7_b14_r7_w1_h12_mass12_shapeRectangle_scalex1_scaley12, transform(all)). | |
| % Example 2 input grid_width10_height20 | |
| object(input2_idP03hft3_t19_l6_b19_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idP03hft3_t13_l6_b13_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idPz7ea0g_t15_l7_b15_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idPz7ea0g_t15_l2_b15_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idP847fa3_t9_l6_b9_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idP847fa3_t9_l3_b9_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idP989a7f_t11_l4_b11_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idP989a7f_t3_l4_b3_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idP33ffe7_t5_l8_b5_r8_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input2_idP33ffe7_t5_l3_b5_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| % Example 2 output grid_width10_height20 | |
| object(output2_idP03hft3_t13_l6_b19_r6_w1_h7_mass7_shapeRectangle_scalex1_scaley7, transform(all)). | |
| object(output2_idPz7ea0g_t15_l7_b15_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(output2_idPz7ea0g_t15_l2_b15_r5_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)). | |
| object(output2_idP847fa3_t9_l5_b9_r6_w2_h1_mass2_shapeRectangle_scalex2_scaley1, transform(all)). | |
| object(output2_idP847fa3_t9_l3_b9_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(output2_idP989a7f_t3_l4_b11_r4_w1_h9_mass9_shapeRectangle_scalex1_scaley9, transform(all)). | |
| object(output2_idP33ffe7_t5_l5_b5_r8_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)). | |
| object(output2_idP33ffe7_t5_l3_b5_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| ``` | |
| There number of output objects may be different than the input objects. | |
| Transformations: sort, gravity towards, rotate, flipx, flipy, move, merge objects, split objects and so on. | |
| Think step by step, what are the transformations across all the examples, that goes from the input to the output. Explain your reasoning for inserting new objects. | |
| With the following example, I want you to predict what the output should be | |
| ```prolog | |
| % Example 3 input grid_width20_height20 | |
| object(input3_idPz7ea0g_t15_l15_b15_r15_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPz7ea0g_t15_l9_b15_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP847fa3_t8_l14_b8_r14_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP847fa3_t8_l8_b8_r8_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPj8kdf4_t10_l10_b10_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPj8kdf4_t3_l10_b3_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP33ffe7_t19_l4_b19_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP33ffe7_t2_l4_b2_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPfe7a8k_t4_l17_b4_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPfe7a8k_t4_l2_b4_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| % Example 3 output grid_width20_height20 | |
| PREDICT the text that starts with object(output3_ | |
| ``` | |
| Repeat the previous example prolog code, with PREDICT replaced with your predictions. | |
| --- | |
| To predict the output of the transformations, we have to understand the transformation pattern from the given examples. Here's the pattern I have observed: | |
| 1. If there are multiple objects with the same id, they merge together either horizontally or vertically. | |
| 2. The direction of merge depends on the Euclidean distance between the objects. If they are closer vertically, they merge vertically and increase their height (y-scale) and mass. If they are closer horizontally, they merge horizontally and increase their width (x-scale) and mass. | |
| 3. The mass of the object after merging is equal to the number of objects merged together. | |
| 4. The new position of the merged object is based on the coordinates of the first object. | |
| Based on this analysis, I can predict the output for the third example as follows: | |
| ```prolog | |
| % Example 3 input grid_width20_height20 | |
| object(input3_idPz7ea0g_t15_l15_b15_r15_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPz7ea0g_t15_l9_b15_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP847fa3_t8_l14_b8_r14_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP847fa3_t8_l8_b8_r8_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPj8kdf4_t10_l10_b10_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPj8kdf4_t3_l10_b3_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP33ffe7_t19_l4_b19_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idP33ffe7_t2_l4_b2_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPfe7a8k_t4_l17_b4_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| object(input3_idPfe7a8k_t4_l2_b4_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)). | |
| % Example 3 output grid_width20_height20 | |
| object(output3_idPz7ea0g_t15_l9_b15_r15_w7_h1_mass7_shapeRectangle_scalex7_scaley1, transform(all)). | |
| object(output3_idP847fa3_t8_l8_b8_r14_w7_h1_mass7_shapeRectangle_scalex7_scaley1, transform(all)). | |
| object(output3_idPj8kdf4_t3_l10_b10_r10_w1_h8_mass8_shapeRectangle_scalex1_scaley8, transform(all)). | |
| object(output3_idP33ffe7_t2_l4_b19_r4_w1_h18_mass18_shapeRectangle_scalex1_scaley18, transform(all)). | |
| object(output3_idPfe7a8k_t4_l2_b4_r17_w16_h1_mass16_shapeRectangle_scalex16_scaley1, transform(all)). | |
| ``` | |
| This prediction follows the pattern observed in the previous examples: | |
| - Objects with the same id have been merged. | |
| - The direction of the merge (horizontal or vertical) is determined by their proximity. | |
| - The mass of the new object is equal to the number of merged objects. | |
| - The position of the new object is based on the coordinates of the first object. | |